An examination of the relationship between time‐domain integral chargeability and the Cole‐Cole impedance model

Geophysics ◽  
1995 ◽  
Vol 60 (4) ◽  
pp. 1249-1252 ◽  
Author(s):  
Kenneth Duckworth ◽  
H. Thomas Calvert
Keyword(s):  
Electrical Properties ◽  
Frequency Dependence ◽  
Time Constant ◽  
Time Domain ◽  
Induced Polarization ◽  
Dc Resistivity ◽  
Impedance Model ◽  
Domain Integral ◽  
The Relationship

The Cole‐Cole impedance model developed in Pelton et al. (1978) for describing the induced polarization (IP) phenomenon has proven to be useful for characterizing the electrical properties of rocks. The model characterizes the impedance Z(ω) of a rock using only four parameters as follows [Formula: see text] where [Formula: see text] is the DC resistivity, m is the dimensionless chargeability, τ is the time constant, c is the frequency dependence, and [Formula: see text] [Formula: see text]

3D numerical modeling of induced-polarization electromagnetic response based on the finite-difference time-domain method

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. E385-E398 ◽  
Author(s):  
Yanju Ji ◽  
Yanqi Wu ◽  
Shanshan Guan ◽  
Xuejiao Zhao
Keyword(s):  
Frequency Dependence ◽  
Impulse Response ◽  
Time Constant ◽  
Time Domain ◽  
Characteristic Time ◽  
Induced Polarization ◽  
Order System ◽  
Ohm’S Law ◽  
Ohm's Law ◽  
Cole Model

Induced-polarization (IP) effects have a significant influence on transient electromagnetic (TEM) data, which commonly manifest a reversed sign. Polarization media usually have a very high economic value. To study the IP effects, a new method for modeling the time-domain electromagnetic signals of 3D dispersive materials is developed. Due to the fractional time derivatives, two main difficulties are needed to be conquered: the derivation of Cole-Cole model impulse response function and the discrete recursion of convolution in Ohm’s law. We use a frequency-domain rational approximation method and the linear programming technique to transfer the fractional order system into an integer order system. This method enables us to achieve a relatively simple and high-precision solution of the Cole-Cole model impulse response. A discrete recursion method for Ohm’s law convolution is proposed to realize an efficient numerical simulation of 3D polarization media by eliminating the prohibitive computing demands. Comparisons with published methods demonstrate the accuracy and efficiency of our algorithm. The characteristic time constant and chargeability have monotonic influences on the IP effects, whereas the frequency dependence indicates a nonmonotonic influence on the IP effects. The negative response is more significant when the frequency dependence is in the midrange. For a 3D low-resistivity chargeable body, a larger size reduces the decay rate of the induced field, which contributes to the obscuration of the polarization field. The middle-sized chargeable body can be detected under certain conditions: high chargeability, millisecond characteristic time constant, and middle frequency dependence. Small-sized chargeable bodies cannot be recognized at all by using the current forward-modeling method and instrument, which highlights the significance of precision improvement.

Spectral induced polarization parameters as determined through time‐domain measurements

Geophysics ◽  
1984 ◽  
Vol 49 (11) ◽  
pp. 1993-2003 ◽  
Author(s):  
Ian M. Johnson
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Field Trials ◽  
Induced Polarization ◽  
Polarization Data ◽  
Forward Solution ◽  
Spectral Parameters ◽  
Impedance Model ◽  
Measurement And Analysis ◽  
The Time Domain

A method for the extraction of Cole-Cole spectral parameters from time‐domain induced polarization data is demonstrated. The instrumentation required to effect the measurement and analysis is described. The Cole-Cole impedance model is shown to work equally well in the time domain as in the frequency domain. Field trials show the time‐domain method to generate spectral parameters consistent with those generated by frequency‐domain surveys. This is shown to be possible without significant alteration to field procedures. Cole-Cole time constants of up to 100 s are shown to be resolvable given a transmitted current of a 2 s pulse‐time. The process proves to have added usefulness as the Cole-Cole forward solution proves an excellent basis for quantifying noise in the measured decay.

scholarly journals Physical Modeling on Time Domain Induced Polarization (TDIP) Response of Metal Mineral Content

2018 ◽  
Vol 8 (2) ◽  
pp. 57
Author(s):  
Yatini Yatini ◽  
Djoko Santoso ◽  
Agus Laesanpura ◽  
Budi Sulistijo
Keyword(s):  
Time Domain ◽  
Physical Modeling ◽  
Iron Ore ◽  
Mineral Content ◽  
Quantitative Relationship ◽  
Physical Modelling ◽  
Induced Polarization ◽  
Physical Models ◽  
Resistivity Method ◽  
The Relationship

The Induced Polarization (IP) methods is an extension of resistivity method by adding ability of the ground in storing electrical charge. One of the measurement technique is done in time domain, hereinafter referred to as Time Domain Induced Polarization (TDIP). TDIP responses measured on the surface are affected by the physical properties of the subsurface. Research in TDIP response modeling studies is performed to obtain a quantitative relationship between response to metallic mineral content at subsurface. The relationship can be obtained by forward and physical modelling. The forward modeling produces a curve that connects TDIP response to the subsurface parameters and an array. The laboratory-scale physical model is performed on the sand-box size (200x100x70) cm3 by varying iron-ore content in a sphere target. TDIP response measurements on physical models is done using Dipole-dipole and Wenner configuration. The relationship between the TDIP response and metal mineral content is obtained by comparing the results of measurements on physical modeling and forward modelling. There is good appropriatement between the theoretical curves and measuring results of the physical modelling. The greater of iron-ore content on the target, increasing in the TDIP response.

Inversions of time-domain spectral induced polarization data using stretched exponential

2019 ◽  
Vol 219 (3) ◽  
pp. 1851-1865
Author(s):  
Seogi Kang ◽  
Douglas W Oldenburg
Keyword(s):  
Time Constant ◽  
Time Domain ◽  
Induced Polarization ◽  
Small Time ◽  
Mineral Deposit ◽  
The Body ◽  
Stretched Exponential ◽  
Simultaneous Inversion ◽  
Spectral Induced Polarization ◽  
Alteration Halo

SUMMARY We provide a two-stage approach to extract spectral induced polarization (SIP) information from time-domain IP data. In the first stage we invert dc data to recover the background conductivity. In the second, we solve a linear inverse problem and invert all time channels simultaneously to recover the IP parameters. The IP decay curves are represented by a stretched exponential (SE) rather than the traditional Cole–Cole model, and we find that defining the parameters in terms of their logarithmic values is advantageous. To demonstrate the capability of our simultaneous SIP inversion we use synthetic data simulating a porphyry mineral deposit. The challenge is to image a mineral body that is hosted within an alteration halo having the same chargeability but a different time constant. For a 2-D problem, we were able to distinguish the body using our simultaneous inversion but we were not successful in using a sequential (or conventional) SIP inversion approach. For the 3-D problem we recovered 3-D distributions of the SIP parameters and used those to construct a 3-D rock model having four rock units. Three chargeable units were distinguished. The compact mineralization zone, having a large time constant, was distinguished from the circular alteration halo that had a small time constant. Finally, to promote the use of the SIP technique, and to have further development of SIP inversion, all examples presented in this paper are available in our open source resources (https://github.com/simpeg-research/kang-2018-spectral-inducedpolarization).

Fast Time Domain Integral Equation Solvers for Large-Scale Electromagnetic Analysis

2004 ◽  
Author(s):  
Eric Michielsssen ◽  
Weng C. Chew ◽  
Jianming Jin ◽  
Balasubramaniam Shanker
Keyword(s):  
Integral Equation ◽  
Time Domain ◽  
Large Scale ◽  
Electromagnetic Analysis ◽  
Fast Time ◽  
Domain Integral ◽  
Time Domain Integral Equation
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